Cluster physical

The gelation transition is observable for Ng > 10. Otherwise, the material behaves as a liquid (Ng < 1). Little is known about materials near Ng = 1. For the following, we consider only materials with iVg 1 and treat them just like chemical gels. The expression T(n + 1, (t — t )/Xpg)/T(n + 1) in Eq. 5-2 approaches a value of one in this case of Ng g> 1, and the critical gel equation, Eq. 4-1, is recovered. However, much work is needed to understand the role of non-permanent physical clusters on network formation and rheological properties. 

A. R. Allnatt and E. Loftus,. Chem. Phys., 59, 2550 (1973). Physical Cluster Theory of Point Defect Interactions. II. Application to AgCl Doped with CdCl2. 

W.C. Swope, H.C. Andersen, P.H. Berens and K.R. Wilson, A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules Application to small water clusters, J. Chem. Phys., 76 (1982) 637. 

A Computer Simulation Method for the Calculation of Equilibrium Constants for the Formation of Physical Clusters of Molecules Application to Small Water Clusters. 

IIL PHYSICAL CLUSTERS IN A VAPOR AND THE EVALUATION OF THEIR PROPERTIES... 

Kusaka I, Wang ZG, Seirrfeld JH (1998a) Direct evalrration of the equilibrium distribution of physical clusters by a grand canonical Monte Carlo simrrlation. J Chem Phys 108 3416-3423 Kusaka I, Wang ZG, Seinfeld JH (1998b) Binary nucleation of sulfuric acid-water Monte Carlo simulation. J Chem Phys 108 6829-6848... 

The key idea is the concept of the physical cluster originated by Hill. ... 

A detailed cloning and sequence study of the VK21 gene family of BALB/c mice also showed that highly homologous VK genes are physically clustered [46], It should be stressed, however, that family member interspersion of some degree has not been ruled out by any experiments to date. 

One must be cautious in equating this statistical quantity with physical clusters. For example, the fact that a polymer chain is a cluster of volume elements means that small molecules mixed with it must be clustered in a complementary way. The application of Equation 2 to the Flory-Huggins equation for a 0 solution leads to an apparent cluster size of (l-[Pg.434]

As a consequence, a similar behaviour, not only at the gel point, but also over the whole range of extent of cross-linking for permanently cross-linked as well as for physical clustered systems, can be expected. 

Swindoll R D and J M Haile 1984. A Mul tiple Time-step Method for Molecular Dynamics Simulations of Fluids of Chain Molecules. Journal of Compututational Physics 53.289-298 Swope W C, H C Anderson, P H Berens and K R Wilson 1982. A Computer Simulation Method for the Calculation of EquBibri-um Constants for the Formation of Physical Clusters of Molecules Application to Small Water Clusters Journal of Chemical Physics 76.637-649 Tobias D J and C L Brooks III 1988 Molecular Dynamics with Internal Coordinate Constraints. Journal of Chemical Physics 89-5115-5126... 

Q is the cluster partition function for a single physical cluster of size n on a lattice with a total of M sites and at temperature T. The summation is over all possible connected physical clusters and 17" is the energy of each such cluster as given by Eq. (1). It should be noted that the summation in Q includes all the M placings of each distinct cluster on the lattice. The result (4) only applies at sufficiently low coneentrations that the clusters do not interact (i.e., the system is ideal) and we assume for the purposes of this further analysis that this is an acceptable approximation up to concentrations of the order of... 

Physical clustering, long-wavelength concentration fluctuations, and microphase separation of self-assembling block copolymers and surfactantlike chain molecules. These systems are discussed in the next section. 

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